1. bookVolume 6 (2019): Issue 12 (December 2019)
Journal Details
License
Format
Journal
eISSN
2182-1976
First Published
16 Apr 2016
Publication timeframe
2 times per year
Languages
English
Open Access

Crazy Sequential Representations of Numbers for Small Bases

Published Online: 07 Feb 2020
Volume & Issue: Volume 6 (2019) - Issue 12 (December 2019)
Page range: 33 - 48
Journal Details
License
Format
Journal
eISSN
2182-1976
First Published
16 Apr 2016
Publication timeframe
2 times per year
Languages
English
Abstract

Throughout history, recreational mathematics has always played a prominent role in advancing research. Following in this tradition, in this paper we extend some recent work with crazy sequential representations of numbers− equations made of sequences of one through nine (or nine through one) that evaluate to a number. All previous work on this type of puzzle has focused only on base ten numbers and whether a solution existed. We generalize this concept and examine how this extends to arbitrary bases, the ranges of possible numbers, the combinatorial challenge of finding the numbers, efficient algorithms, and some interesting patterns across any base. For the analysis, we focus on bases three through ten. Further, we outline several interesting mathematical and algorithmic complexity problems related to this area that have yet to be considered.

Keywords

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